It's a well-known result that the 2d tomography problem is weakly ill-posed even with full data and strongly ill-posed if you don't have complete angular coverage.

With respect to discrete samples and a discretized model for the density in the area being scanned, you'd have to regularize the solution (or use a coarse discretization which effectively regularizes the solution.) You can then analyze the resolution of the regularized solution. However, the resolution matrix isn't a measure of bias in the solution and you can't bound the bias without making assumptions about the smoothness of the solution.

Could you edit your question to add more context? What exactly are you trying to do?

It's a well-known result that the 2d tomography problem is weakly ill-posed (singular values decay as $O(1/\sqrt{n})$ even with full data and strongly ill-posed (the singular values decay exponentially) if you don't have complete angular coverage.

See for example:

M. E. Davison. The Ill-Conditioned Nature of the Limited Angle Tomography Problem. SIAM Journal on Applied Mathematics 42(3):428-448, 1983. https://doi.org/10.1137/0143028

With respect to discrete samples and a discretized model for the density in the area being scanned, you'd have to regularize the solution (or use a coarse discretization which effectively regularizes the solution.) You can then analyze the resolution of the regularized solution. However, the resolution matrix isn't a measure of bias in the solution and you can't bound the bias without making assumptions about the smoothness of the solution.

Could you edit your question to add more context? What exactly are you trying to do?

It's a well-known result that the problem is ill-posed if you don't have complete angular coverage.

With respect to discrete samples and a discretized model for the density in the area being scanned, you'd have to regularize the solution (or use a coarse discretization which effectively regularizes the solution.) You can then analyze the resolution of the regularized solution. However, the resolution matrix isn't a measure of bias in the solution and you can't bound the bias without making assumptions about the smoothness of the solution.

Could you edit your question to add more context? What exactly are you trying to do?

It's a well-known result that the 2d tomography problem is weakly ill-posed even with full data and strongly ill-posed if you don't have complete angular coverage.

With respect to discrete samples and a discretized model for the density in the area being scanned, you'd have to regularize the solution (or use a coarse discretization which effectively regularizes the solution.) You can then analyze the resolution of the regularized solution. However, the resolution matrix isn't a measure of bias in the solution and you can't bound the bias without making assumptions about the smoothness of the solution.

Could you edit your question to add more context? What exactly are you trying to do?